Abate, Joseph; Whitt, Ward Transient behavior of regulated Brownian motion. I: Starting at the origin. (English) Zbl 0628.60083 Adv. Appl. Probab. 19, 560-598 (1987). This paper is the first of a series of two, studying the transient behaviour of regulated (that is to say, reflected) Brownian motion R as a model for the transient behaviour of stochastic flow systems. The objective is to obtain simple approximations for the moments of R. This paper considers the special case when R begins at zero. After a lengthy discussion of results, an exposition is given of the construction of R using Skorokhod’s “reflecting barrier function”. Various probabilistic and Laplace-transform arguments are then applied, culminating in proposals for approximation of normalized moment functions by mixtures of exponentials. It is notable that the relaxation-time exponential approximation does not provide a useful fit for moderate time values. Reviewer: W.S.Kendall Cited in 2 ReviewsCited in 38 Documents MSC: 60J65 Brownian motion 60J60 Diffusion processes Keywords:inverse Gaussian distribution; complete monotonicity; transient behaviour of stochastic flow systems; simple approximations for the moments; reflecting barrier function; Laplace-transform arguments; relaxation-time Software:Algorithm 619 PDFBibTeX XMLCite \textit{J. Abate} and \textit{W. Whitt}, Adv. Appl. Probab. 19, 560--598 (1987; Zbl 0628.60083) Full Text: DOI